According to an article in the Financial Times, the firms will be looking to raise in the region of â¬30 billion ($37.3 billion) of additional equity between them.
One unnamed executive at an investment bank in the territory told the newspaper that it may not only be the firms found to be in the weakest position that prepare recapitalization efforts.
"The top three or four banks in Europe should be thinking: 'How do I make myself bullet-proof?'," he stated.
Publication of the stress tests is expected to be made on July 23rd 2010, with the results of examinations on around 100 banks to be reported.
The test has been toughened up, with tier one capital now required to stand at six per cent to pass the examination, rather than the four per cent level previously employed.
Earlier this week, Axel Weber, head of the Bundesbank in Germany, told banks in the country to prepare a strategy for emergency-capital raising in the event of them failing their stress test.
A banker present at the meeting of the 16 chief executives from the country's top financial institutions said that they were told potential recapitalization could occur "either with the help of their owners or with the help of the German bank rescue fund".
"In effect, this will lead to forced recapitalizations of such banks," the insider added.
Speaking prior to the agreement that was made to publish the stress test results last month, Josef Ackermann, the chief executive officer of Deutsche Bank, warned that such a strategy could be "very, very dangerous".
He stated that market instability and uncertainty could well be increased by public knowledge of the results unless appropriate "backstop facilities" were implemented prior to publication.
By Claire Archer